If someone creates a barrier and I hit that figure and knock them off their barrier clicks, does the barrier come down?
Thanks

Yep, for the same reason that if you knock an outwitter off of outwit, your outwitted power returns.

BTW--Mystic damage and Crit Miss damage happens at the end of the action, right? E.G. if I were using HSS option 1, on my last click of hypersonic speed, I would wait until the action resolves (finish running away) before the click occurs.

Citical miss and Mystics damage are applied immediately, so it is possible to knock yourself off HSS or have fewer squares left to move if your character's Speed value drops and it keeps HSS.

No way! Good thing that decision didn't affect the game...